MathDB
2022 B Individual #21

Source:

April 30, 2022
2022 B Individual

Problem Statement

A herder has forgotten the number of cows she has, and does not want to count them all of them. She remembers these four facts about the number of cows:
[*]It has 33 digits. [*]It is a palindrome. [*]The middle digit is a multiple of 44. [*]It is divisible by 1111.
What is the sum of all possible numbers of cows that the herder has?
<spanclass=latexbold>(A)</span>343<spanclass=latexbold>(B)</span>494<spanclass=latexbold>(C)</span>615<spanclass=latexbold>(D)</span>635<spanclass=latexbold>(E)</span>726<span class='latex-bold'>(A) </span>343\qquad<span class='latex-bold'>(B) </span>494\qquad<span class='latex-bold'>(C) </span>615\qquad<span class='latex-bold'>(D) </span>635\qquad<span class='latex-bold'>(E) </span>726